Decoupling relations to O(αs3) and their connection to low-energy theorems

If quantum chromodynamics (QCD) is renormalized by minimal subtraction (MS), at higher orders, the strong coupling constant alpha(s) and the quark masses m(q) exhibit discontinuities at the flavour thresholds, which are controlled by so-called decoupling constants, zeta(g) and zeta(m), respectively. Adopting the modified MS (MS) scheme, we derive simple formulae which reduce the calculation of zeta(g) and zeta(m) to the solution of vacuum integrals. This allows us to evaluate zeta(g) and zeta(m) through three loops. We also establish low-energy theorems, valid to all orders, which relate the effective couplings of the Higgs boson to gluons and light quarks, due to the virtual presence of a heavy quark h, to the logarithmic derivatives with respect to m(h) of zeta(g) and zeta(m), respectively. Fully exploiting the present knowledge of the anomalous dimensions of alpha(s) and m(q), we thus calculate these effective couplings through four loops. Finally, we perform a similar analysis for the coupling of the Higgs boson to photons. (C) 1998 Elsevier Science B.V.